For a laminate with N layers, the (3×3) is defined as:
When the above code is completed with a correct B matrix, running it for a 0.2m square, 5mm thick, [0/90/90/0] graphite/epoxy plate under 1000 Pa gives: Composite Plate Bending Analysis With Matlab Code
[σ1σ2τ12]=[Q11Q120Q12Q22000Q66][ϵ1ϵ2γ12]the 3 by 1 column matrix; sigma sub 1, sigma sub 2, tau sub 12 end-matrix; equals the 3 by 3 matrix; Row 1: cap Q sub 11, cap Q sub 12, 0; Row 2: cap Q sub 12, cap Q sub 22, 0; Row 3: 0, 0, cap Q sub 66 end-matrix; the 3 by 1 column matrix; epsilon sub 1, epsilon sub 2, gamma sub 12 end-matrix; Where the reduced stiffness components ( Qijcap Q sub i j end-sub ) are calculated from the engineering constants: For a laminate with N layers, the (3×3)
The script will output the maximum central deflection in millimeters and display the -matrix ( Dijcap D sub i j end-sub For a laminate with N layers
clear; clc; close all;
For a comprehensive guide on Composite Plate Bending Analysis , the article Analysis of composites laminates using MATLAB (available via